UNIT 5 : TIME VALUE OF MONEY Flashcards
You have determined the profitability of a planned project by findingthe present value of all the cash flows from that project. Which of thefollowing would cause the project to look more appealing in terms of thepresent value of those cash flows?
a. The discount rate decreases.
b. The cash flows are extended over a longer period of time, but thetotal amount of the cash flows remains the same.
c. The discount rate increases.
d. Statements b and c are correct.
e. Statements a and b are correct.
A
Which of the following statements is most correct?
a. A 5-year $100 annuity due will have a higher present value than a5-year $100 ordinary annuity.
b. A 15-year mortgage will have larger monthly payments than a 30-yearmortgage of the same amount and same interest rate.
c. If an investment pays 10 percent interest compounded annually, itseffective rate will also be 10 percent.
d. Statements a and c are correct.
e. All of the statements above are correct.
E
The future value of a lump sum at the end of five years is $1,000. Thenominal interest rate is 10 percent interest is and compoundedsemiannually. Which of the following statements is most correct?
a. The present value of the $1,000 is greater if interest is compoundedmonthly rather than semiannually.
b. The effective annual rate is greater than 10 percent.
c. The periodic interest rate is 5 percent.
d. Statements b and c are correct.
e. All of the statements above are correct.
D
Which of the following statements is most correct?
a. The present value of an annuity due will exceed the present value ofan ordinary annuity (assuming all else equal).
b. The future value of an annuity due will exceed the future value of anordinary annuity (assuming all else equal).
c. The nominal interest rate will always be greater than or equal to theeffective annual interest rate.
d. Statements a and b are correct.
e. All of the statements above are correct.
D
Which of the following investments will have the highest future value atthe end of 5 years? Assume that the effective annual rate for allinvestments is the same.
a. A pays $50 at the end of every 6-month period for the next 5 years (atotal of 10 payments).
b. B pays $50 at the beginning of every 6-month period for the next5 years (a total of 10 payments).
c. C pays $500 at the end of 5 years (a total of one payment).
d. D pays $100 at the end of every year for the next 5 years (a total of5 payments).
e. E pays $100 at the beginning of every year for the next 5 years (atotal of 5 payments).
E
Which of the following bank accounts has the highest effective annualreturn?
a. An account that pays 10 percent nominal interest with monthly compounding.
b. An account that pays 10 percent nominal interest with daily compounding.
c. An account that pays 10 percent nominal interest with annual compounding.
d. An account that pays 9 percent nominal interest with daily compounding.
e. All of the investments above have the same effective annual return.
B
You are interested in investing your money in a bank account. Which ofthe following banks provides you with the highest effective rate ofinterest?
a. Bank 1; 8 percent with monthly compounding.
b. Bank 2; 8 percent with annual compounding.
c. Bank 3; 8 percent with quarterly compounding.
d. Bank 4; 8 percent with daily (365-day) compounding.
e. Bank 5; 7.8 percent with annual compounding.
D
Your family recently obtained a 30-year (360-month) $100,000 fixed-ratemortgage. Which of the following statements is most correct? (ignore all taxes and transaction costs.)
a. The remaining balance after three years will be $100,000 less thetotal amount of interest paid during the first 36 months.
b. The proportion of the monthly payment that goes towards repayment ofprincipal will be higher 10 years from now than it will be this year.
c. The monthly payment on the mortgage will steadily decline over time.
d. All of the statements above are correct.
e. None of the statements above is correct.
B
Frank Lewis has a 30-year, $100,000 mortgage with a nominal interestrate of 10 percent and monthly compounding. Which of the followingstatements regarding his mortgage is most correct?
a. The monthly payments will decline over time.
b. The proportion of the monthly payment that represents interest willbe lower for the last payment than for the first payment on the loan.
c. The total dollar amount of principal being paid off each month getslarger as the loan approaches maturity.
d. Statements a and c are correct.
e. Statements b and c are correct.
E
Your bank account pays an 8 percent nominal rate of interest. Theinterest is compounded quarterly. Which of the following statement is most correct?
a. The periodic rate of interest is 2 percent and the effective rate ofinterest is 4 percent.
b. The periodic rate of interest is 8 percent and the effective rate ofinterest is greater than 8 percent.
c. The periodic rate of interest is 4 percent and the effective rate ofinterest is 8 percent.
d. The periodic rate of interest is 8 percent and the effective rate ofinterest is 8 percent.
e. The periodic rate of interest is 2 percent and the effective rate ofinterest is greater than 8 percent.
E
Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?
a. The present value of the ordinary annuity must exceed the presentvalue of the annuity due, but the future value of an ordinary annuitymay be less than the future value of the annuity due.
b. The present value of the annuity due exceeds the present value of theordinary annuity, while the future value of the annuity due is lessthan the future value of the ordinary annuity.
c. The present value of the annuity due exceeds the present value of theordinary annuity, and the future value of the annuity due alsoexceeds the future value of the ordinary annuity.
d. If interest rates increase, the difference between the present valueof the ordinary annuity and the present value of the annuity dueremains the same.
e. Statements a and d are correct.
C
A $10,000 loan is to be amortized over 5 years, with annual end-of-yearpayments. Given the following facts, which of these statements is most correct?
a. The annual payments would be larger if the interest rate were lower.
b. If the loan were amortized over 10 years rather than 5 years, and ifthe interest rate were the same in either case, the first paymentwould include more dollars of interest under the 5-year amortizationplan.
c. The last payment would have a higher proportion of interest than thefirst payment.
d. The proportion of interest versus principal repayment would be thesame for each of the 5 payments.
e. The proportion of each payment that represents interest as opposed torepayment of principal would be higher if the interest rate werehigher.
E
Which of the following is most correct?
a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary annuity. (Assume that both annuities pay$100 per period and there is no chance of default.)
b. If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 percent.
c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same.
d. Statements a and c are correct.
e. All of the statements above are correct.
E
Which of the following statements is most correct?
a. An investment that compounds interest semiannually, and has a nominalrate of 10 percent, will have an effective rate less than 10 percent.
b. The present value of a 3-year $100 annuity due is less than thepresent value of a 3-year $100 ordinary annuity.
c. The proportion of the payment of a fully amortized loan that goestoward interest declines over time.
d. Statements a and c are correct.
e. None of the statements above is correct.
C
Which of the following statements is most correct?
a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.
b. If you are lending money, then, based on effective interest rates,you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments.However, as a borrower you should prefer the annual payment loan
c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero.
d. Statements b and c are correct.
e. All of the statements above are correct.
E
